A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements

We consider mixed finite element discretizations of linear second order ell iptic boundary value problems with respect to an adaptively generated hiera rchy of possibly highly nonuniform simplicial triangulations. In particular , we present and analyze four different kinds of error estimators: a residu al based estimator, a hierarchical one, error estimators relying on the sol ution of local subproblems and on a superconvergence result, respectively. finally, we examine the relationship between the presented error estimators and compare their local components.